Question

An ideal turbofan with a bypass ratio of 5 has core mass flow rate, \( \dot{m}_a,c = 100 \, {kg/s} \). The core and the fan exhausts are separate and optimally expanded. The core exhaust speed is 600 m/s and the fan exhaust speed is 120 m/s. If the fuel mass flow rate is negligible in comparison to \( \dot{m}_a,c \), the static specific thrust (\( \frac{T}{\dot{m}_a,c} \)) developed by the engine is _________ Ns/kg (rounded off to the nearest integer).

Hint:

The static specific thrust is the difference between the exhaust velocity and free-stream velocity, normalized by the core mass flow rate.

Answer 1

Given Parameters
 

• Bypass Ratio (BPR) = 5
• Core air mass flow rate: \( \dot{m}_{a,c} = 100 \, \text{kg/s} \)
• Fan air mass flow rate: \( \dot{m}_{a,f} = \text{BPR} \times \dot{m}_{a,c} = 5 \times 100 = 500 \, \text{kg/s} \)
• Core exhaust velocity: \( V_{e,c} = 600 \, \text{m/s} \)
• Fan exhaust velocity: \( V_{e,f} = 120 \, \text{m/s} \)
• Flight velocity (inlet speed): \( V_0 = 0 \, \text{m/s} \)

Step 1: Calculate Total Thrust
Thrust is the sum of the momentum contributions from the core and bypass (fan) streams:
\[ T = \dot{m}_{a,c} (V_{e,c} - V_0) + \dot{m}_{a,f} (V_{e,f} - V_0) \] \[ T = 100 \times 600 + 500 \times 120 = 60000 + 60000 = 120000 \, \text{N} \]

Step 2: Calculate Static Specific Thrust

Final Answer:
\[ \boxed{1200} \]